Advertisements
Advertisements
प्रश्न
What is the polar form of the complex number (i25)3?
उत्तर
z = (i25)3
= (i)75
= `i^(4 xx 18 + 3)`
= (i4)18 (i)3
= i3 = –i = 0 – i
Polar form of z = r(cosθ + isinθ)
= `1{cos(- pi/2) + isin(- pi/2)}`
= `cos pi/2 - i sin pi/2`
APPEARS IN
संबंधित प्रश्न
Find the modulus and the argument of the complex number `z = – 1 – isqrt3`
Find the modulus and the argument of the complex number `z =- sqrt3 + i`
Convert the given complex number in polar form: 1 – i
Convert the given complex number in polar form: – 1 + i
Convert the given complex number in polar form: –3
Convert the given complex number in polar form `sqrt3 + i`
Convert the given complex number in polar form: i
Convert the following in the polar form:
`(1+3i)/(1-2i)`
If |z| = 2 and arg(z) = `pi/4`, then z = ______.
The locus of z satisfying arg(z) = `pi/3` is ______.
The amplitude of `sin pi/5 + i(1 - cos pi/5)` is ______.
If arg(z – 1) = arg(z + 3i), then find x – 1 : y. where z = x + iy.
If for complex numbers z1 and z2, arg (z1) – arg (z2) = 0, then show that `|z_1 - z_2| = |z_1| - |z_2|`.
Write the complex number z = `(1 - i)/(cos pi/3 + i sin pi/3)` in polar form.
arg(z) + arg`barz (barz ≠ 0)` is ______.
If |z| = 4 and arg(z) = `(5pi)/6`, then z = ______.
State True or False for the following:
Let z1 and z2 be two complex numbers such that |z1 + z2| = |z1| + |z2|, then arg(z1 – z2) = 0.
Find z if |z| = 4 and arg(z) = `(5pi)/6`.
|z1 + z2| = |z1| + |z2| is possible if ______.
The value of arg (x) when x < 0 is ______.